Question

Which of the following is not a rational number?
\[
  A.{\text{ }}\dfrac{0}{1} \\
  B.{\text{ }}\dfrac{1}{0} \\
  C.{\text{ }}\dfrac{0}{3} \\
  D.{\text{ }}\dfrac{0}{2} \\
\]

Answer 1

Hint: In order to solve the problem use the basic definition of rational number and check for all the options, which of them does not fulfil the criterion of rational number.

Complete step-by-step answer:
We will check each option according to the definition of rational number.
Rational number is a number that can be expressed as the quotient or fraction $\dfrac{p}{q}$ of two integers, a numerator p and a non-zero denominator q.
Consider option A
$\dfrac{0}{1}$ is written in $\dfrac{p}{q}$ form, where q is non zero denominator so it is defined.
$\dfrac{0}{1}$ is a rational number

Take option B
$\dfrac{1}{0}$ is written in $\dfrac{p}{q}$ form, but here denominator is zero, which is not defined in mathematics
$\dfrac{1}{0}$ is not a rational number

Take option C
$\dfrac{0}{3}$ is written in $\dfrac{p}{q}$ form, where q is non zero denominator so it is defined
$\dfrac{0}{3}$ is a rational number

Take option D
$\dfrac{0}{2}$ is written in $\dfrac{p}{q}$ form, where q is non zero denominator so it is defined
$\dfrac{0}{2}$ is a rational number
Hence, $\dfrac{1}{0}$ is not a rational number.
So, option B is the correct answer.

Note- Rational number is a number that can be expressed as the quotient or fraction $\dfrac{p}{q}$ of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. But every rational number is not an integer.